FM modulated waves that are widely used in FM radio broadcasting and television broadcasting are signals in which a sine-wave carrier signal is subjected to phase modulation by a music signal. FM modulated waves have high resistance against noise and can transmit music signals having a wide band of 15 kHz with a low distortion factor. However, in multipath propagation paths that include, in addition to paths by which radio waves arrive directly, paths by which radio waves arrive with a delay due to reflection by obstructions such as buildings, the influence of strong reflected waves received together with direct waves disturbs the phase information required for demodulation, and distortion therefore occurs in the demodulated signal. This distortion that is produced as a result of multipath propagation paths is referred to as “multipath distortion.” An equalizer for reducing multipath distortion by compensating for the characteristics of the multipath propagation paths is referred to as a “multipath equalizer” or a “multipath distortion canceller.”
A multipath equalizer reduces the influence of multipaths in the received signal by passing the received signal through a filter having the inverse characteristics of the multipath propagation paths, i.e., an inverse filter. The characteristics of the multipath propagation paths change according to the environment, and the characteristics of the inverse filter must therefore be optimized according to conditions over time. As a result, adaptive digital filters are typically used for inverse filters.
An adaptive digital filter is a filter having a capability for automatically updating filter coefficients according to changes in the environment. An algorithm for calculating filter coefficients at each point in time is referred to as an “adaptive algorithm,” an LMS (Least Mean Square) algorithm being a representative example. In a broad sense, an LMS algorithm is a method of minimizing the mean-square error based on a steepest-descent method and offers the advantages of stability and a small amount of operations. An adaptive algorithm known as a “complex LMS algorithm” is also known. A complex LMS algorithm is an expansion of the LMS algorithm for cases in which each of the input signal, output signal, target signal, and filter coefficients are complex amounts, and such an algorithm is used, for example, when the input is a narrow-band high-frequency signal and adaptation is realized by separating the in-phase component and quadrature component of the input signal.
A conventional equalizer that is realized through the use of an adaptive digital filter requires a reference signal (training signal) for adaptation, and this requirement tends to bring about a reduction of communication efficiency due to interruptions in communication and the effect of redundant reference signals. In contrast, an equalizer known as a “blind equalizer” that has been developed in recent years performs restorative equalization of signals based only on the received signals without requiring a reference signal for adaptation. Algorithms suitable for such blind equalization are referred to as “blind algorithms,” a CMA (Constant Modulus Algorithm) being a representative example.
As disclosed in the document C. Richard Johnson, Jr., Philip Schniter, Thomas J. Endres, James D. Behm, Donald R. Brown, and Raúl A. Casas, “Blind Equalization Using the Constant Modulus Criterion: A Review” (Proceedings of IEEE, Vol. 86, No. 10, October 1998), CMA typically refers to an algorithm that takes as an index a statistic relating to the output signal such as the envelope of the filter output or a higher-order statistic and that updates filter coefficients such that this index approaches a target value. As disclosed in the document: J. R. Treichler and B. G. Agee, “A New Approach to Multipath Correction of Constant Modulus Signals” (IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 31, No. 2, pp. 459-472, April 1983), when using a constant-amplitude modulated wave in which the amplitude of the modulated wave is fixed, as in FM modulation, the envelope of the filter output, i.e., the amplitude, is used as the index, and the filter coefficients are updated to minimize the error between a target value and the value of the envelope of the signal following passage through the filter. In this way, distortion of phase is corrected together with the correction of distortion of the envelope, and the influence of the reflected waves of multipath propagation paths is eliminated. Here, CMA is a different concept than an adaptive algorithm. In CMA, an adaptive algorithm such as the previously mentioned LMS algorithm is used as an adaptive algorithm for calculating filter coefficients at each time point. In order to control the value of the envelope of the output signal of a filter to a uniform value as described above, the value of the envelope must be extracted instantaneously, and complex signal processing is one representative method. In complex signal processing, a real signal f2 having phase that is delayed 90° (π/2) with respect to a particular real signal f1 is generated by, for example, a Hilbert transformer, whereby a complex signal (typically referred to as an “analytic signal”) having f1 as a real part and f2 as an imaginary part is generated. Thus, the value of the envelope of this real signal can be found instantaneously by calculating the square sum of the real part and imaginary part of the complex signal. However, when the output signal of the filter is subjected to complex signal processing, delay caused by the complex signal processing in the coefficient updating loop gives rise to instability of the loop, and complex signal processing is therefore preferably carried out upon the input signal. In this case, the input signal becomes a complex signal, and an algorithm that can handle complex quantities such as a complex LMS algorithm is therefore used as the adaptive algorithm. This method is hereinbelow referred to as the “first technique of the related art.”
FIG. 1 shows the configuration of an adaptive digital filter that uses the first technique of the related art. Input signal X(k) is a complex signal realized by a Hilbert transformer (not shown). Complex filter coefficient vector W(k) are convoluted with this complex signal as input to obtain output signal y(k), which is a complex signal. Complex filter coefficient vector W(k) are updated by an adaptive algorithm that has been expanded to handle complex signals such that the value of the envelope of output signal y(k) approaches a target value that has been prescribed in advance. The algorithm of this adaptive digital filter is represented as shown below:W(k+1)=W(k)−μ(|y(k)|p−yref0)qy(k)XH(k)  (1)y(k)=WT(k)X(k)  (2)W(k)=[w0(k),w1(k), . . . , wN-1(k)]T  (3)X(k)=[x(k),x(k−1), . . . , x(k−N+1)]T  (4)where W(k) represents a filter coefficient vector, X(k) represents a complex signal vector, k represents a sample index, N represents the number of filter taps, y(k) represents the output signal, yref0 represents the envelope target value, and μ represents a parameter for determining the amount of update of the filter coefficients. In addition, H represents a complex conjugate transposition, and T represents a transposition. The values p and q are constants for determining an evaluation function of error with respect to the envelope target value, and for example, may be p=1 and q=1.
In the first technique of the related art, two signals having phases shifted 90° (π/2) with respect to each other are generated by applying complex signal processing. However, as can be seen from the patent document JP-A-2005-064618 and the document “Hardware Implementation of FM Multipath Distortion Canceller” by Itami Makoto, Hatori Mitsutoshi, and Tsukamoto Norio (National Convention Record of the Institute of Television Engineers of Japan, pp. 355-356, 1986), if sampling is carried out at a frequency of (4/odd number) times the carrier frequency when sampling the input signal, the phases of adjacent sample points will be shifted 90°. By taking this approach, an adaptive algorithm for handling real numbers can be used as is, and the square sum of adjacent sample points can be calculated when seeking the value of the envelope of the output. This method is hereinbelow referred to as the “second technique of the related art.”
FIG. 2 shows the configuration of an adaptive digital filter that uses the second technique of the related art. Input signal Xr(k) is a real signal, and real-signal filter coefficient vector Wr(k) are convoluted with this real signal as input to obtain output signal yr(k) that is a real signal. Filter coefficient vector Wr(k) are updated by an adaptive algorithm that handles real coefficients such that the envelope of output signal yr(k) approaches a target value that has been prescribed in advance. The algorithm of this adaptive digital filter is represented as shown below:Wr(k+1)=Wr(k)=μ(Env[yr(k)]−yref0)yr(k)Xr(k)  (5)yr(k)=WrT(k)Xr(k)  (6)Env[yr(k)]=(yr2(k−1)+yr2(k))1/2  (7)Wr(k)=Re[W(k)]  (8)Xr(k)=Re[X(k)]  (9)where Wr(k) represents a real coefficient vector, Xr(k) represents a real signal vector, Env[ ] represents an operation for obtaining an approximate value of the envelope, Re[ ] represents an operation for extracting the real part of the complex number, and yr(k) represents a real-number output signal. The envelope target value yref0 is basically a constant, but in JP-A-2005-064618, the envelope target value is variably set according to the amplitude of the input signal of the adaptive digital filter to eliminate the influence of Doppler fading contained in a received wave and thus stabilize the adaptive process. More specifically, the input amplitude signal is found by calculating the square sum of adjacent sample points in the input signal, and a signal obtained by passing this input amplitude signal through an LPF (Low-Pass Filter) is then taken as the envelope target value.
The problem of the above-described adaptive digital filter of the related art is the requirement for a large amount of operations and large-scale hardware. The reasons for these problems are as described below.
A first reason is the extremely broad range of fluctuation of filter coefficients. For example, when the envelope target value is “1” and the input signal amplitude is “1,” the filter coefficient have a value on the order of “1,” but when the input signal amplitude is “0.01,” the filter coefficient have a value on the order of “100.” In order to accurately express filter coefficients having this broad range of fluctuation without causing overflow, highly accurate operations are required in filter coefficients operation in which filter coefficients are represented by floating points or, in the case of a fixed point, in which the number of bits is increased. However, high-accuracy operations entail a large amount of operation and increase the scale of hardware.
A second reason is the complex signal processing. In other words, in the adaptive digital filter shown in FIG. 1, almost all signal processing for input signal X(k), filter coefficient vector W(k), and output signal y(k) is carried out by complex numbers. One multiplication between complex numbers is equivalent to four multiplications and two additions of real numbers. In a multipath equalizer for an FM receiver, the convolution operations and coefficients updating operations of a filter having a large number of taps must be carried out for each short sampling cycle, and the amount of operations is therefore voluminous. In the adaptive digital filter shown in FIG. 2, the calculation accuracy of the envelope will be high, performance equivalent to the adaptive digital filter shown in FIG. 1 will be obtained, and the amount of operations can be cut to approximately 25% if the sampling frequency is a precise multiple of (4/odd number) as seen from the center frequency of an intermediate frequency signal. However, severe limitations are placed on the sampling frequency, and this raises the different problem of preventing freedom of design for any sampling frequency. When the sampling frequency diverges from a multiple of (4/odd number) of the center frequency of the intermediate frequency signal, the calculation accuracy of the envelope drops and the performance of the multipath equalizing itself deteriorates.